Just a guess--but cane begonias need a lot of light. I'm betting yours isn't getting enough and is trying to find some. If you notice plants growing outdoors or in nature, in the shade, if they're plants that need more light they go looking for it. Then when they find it they get bushy. I grow most of my canes outside, and they do best when they get some sun. (They also do best when they get some water, which mine don't always get. Do as I say, not as I do.)